@article {3152435, title = {Reactive standard deontic logic}, journal = {Journal of Logic and Computation}, volume = {25}, number = {1}, year = {2013}, pages = {117{\textendash}157}, abstract = {

We introduce a reactive variant of SDL (standard deontic logic): SDLR1 (reactive standard deontic logic). Given a Kripkean view on the semantics of SDL in terms of directed graphs where arrows {\textrightarrow} represent the accessibility relation between worlds, reactive models add two elements: arrows {\textrightarrow} are labelled as ‘active’ or ‘inactive’, and double arrows \&8608; connect arrows, e.g. (x1 {\textrightarrow} x2) \&\#8608; (x3 {\textrightarrow} x4). The idea is that passing through x1 {\textrightarrow} x2 activates a switch represented by \&8608; that inverts the label of x3 {\textrightarrow} x4 and hence activates respectively deactivates this arrow. This allows to introduce two modalities: \&\#9633; is the usual KD-modality of SDL and operates on the Kripkean graph where all labels and double arrows are ignored, while \&\#8709; takes them into account. We demonstrate that RSDL1 allows for an intuitive interpretation of ‘ought’. The logic can handle contrary-to-duty cases such as several instantiations of the Chisholm set in a paradox-free way by means of using double arrows and annotations to block and give access to ideal worlds.

}, issn = {0955-792X}, doi = {http://dx.doi.org/10.1093/logcom/exs043}, author = {Gabbay, Dov M. and Stra{\ss}er, Christian} } @incollection {D:eial, title = {The Need for Adaptive Logics in Epistemology}, booktitle = {Logic, Epistemology, and the Unity of Science}, year = {2004}, pages = {459{\textendash}485}, publisher = {Kluwer}, address = {Dordrecht}, abstract = {

After it is argued that philosophers of science have lost their interest in logic because they applied the wrong type of logics, examples are given of the forms of dynamic reasoning that are central for philosophy of science and epistemology. Adaptive logics are presented as a means to understand and explicate those forms of reasoning. All members of a specific (large) set of adaptive logics are proved to have a number of properties that warrant their formal decency and their suitability with respect to understanding and explicating dynamic forms of reasoning. Most of the properties extend to other adaptive logics.

}, author = {Batens, Diderik}, editor = {Rahman, Shahid and Symons, John and Gabbay, Dov M. and Van Bendegem, Jean Paul} }